International Communications in Heat and Mass Transfer xxx (2014) xxx–xxx
ICHMT-02986; No of Pages 5
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International Communications in Heat and Mass Transfer
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Numerical investigations of developing flow and heat transfer in raccoon typemicrochannels under inlet pulsation☆
Tapas K. Nandi a, Himadri Chattopadhyay b,⁎a Dept. of Mechanical Engg., Techno India College of Technology, Kolkata 700156, Indiab Dept. of Mechanical Engg., Jadavpur University, Kolkata 700032, India
☆ Communicated by W.J. Minkowycz.⁎ Corresponding author.
RThe present study investigates numerically the simultaneously developing unsteady laminar fluid flow and heattransfer inside a two dimensional wavy microchannel caused by a sinusoidal varying velocity component at aninlet. Theflowwas both thermally and hydro dynamically developingwhile the channelwallswere kept at a uni-form temperature. The simulation was performed in the laminar regime for Prandtl number 7(water) and Reyn-olds number ranging from 0.1 to 100. AWavymicrochannel having non-dimensional hydraulic diameter 1 withvarying pulsating amplitude and frequency represented by the Strouhal number was designed for the givenReynolds number range. Based on the comparisonwith steady flow in a wavy channel it was found that imposedsinusoidal velocity at the inlet can provide improved heat transfer performance at different amplitudes (0.2, 0.5,0.8) and frequencies (1, 5, 10) while keeping the pressure drop within acceptable limits.
Heat transfer under pulsating inlet condition is of interest to re-searchers as it is frequently encountered in different engineering prac-tices as well as in bio-fluid systems. Though flow development andheat transfer in channels and ducts is quite well studied, transport phe-nomena in microchannel with pulsating flow condition are yet to befully understood. Active cooling using single phase fluid flow in micro-sized channels is of interest for cooling applications such as electronicequipment, microreactors, microcombusters and micro heat pumps.The different heat transfer enhancement techniques for single phaseflow in microchannels and minichannels are discussed by Marks et al.[1]. One of the passive enhancement techniques thatmay be used to en-hance the heat transfer rate of microchannel is wavy periodic channel.Thereforewavy passages have been considered in several earlier studiesas a means to enhance heat transfer when employed in traditional highReynolds number, presently for low Reynolds number andmicro fluidicsystem by Xin and Tao [2].
A conventional microchannel heat sink generally employs straightchannel in which the streamlines of the coolant are nearly straight.Whereas, in wavy channel a self sustained oscillatory flow is developed.These self sustained oscillation leads to the destabilization of the lami-nar boundary layer which enhances the mixing between the core and
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hattopadhyay, Numerical inmun. Heat Mass Transf. (20
near wall fluid. When liquid flows through curved passages, secondaryflow (Dean Vortices) may be formed. This accelerates the expansionand contraction of the flow element and thus improves the mixing aswell as heat transfer. This mechanism has been studied by many re-searches as Patankar et al. [3], Wang and Yang [4] for improved heattransfer in microchannel. Some artificial means to improve the heattransfer for creeping flows in wavy microchannel was employed bymany researchers such as Quddas et al. [5] and Xia et al. [6]. An experi-ment was carried out by Hsieh and Huang [7] where they inducteddifferent kinds of passive ribs in wavy microchannel for improving theheat transfer at very low Reynolds number (Re b 1). An experimentalstudy was carried out by Sui et al. [8] where they found that theheat transfer performance of the wavy microchannels is comparedwith those of straight baseline microchannels with the same crosssection and length. It is found that the heat transfer performance ofwavy microchannels is much better than that of straight baselinemicrochannels; at the same time the pressure drop penalty of thewavy microchannels can be much smaller than the heat transferenhancement. A numerical and experimental study of flow andheat transfer was carried out by Gong et al. [9] in a wavy microchannelwith hydraulic diameter 500 μm and Reynolds number considered50 b Re b 150. They concluded that wavy surface in microchannelcan be a potential candidate for heat transfer improvement withthe proper selection of geometry and flow parameter without employingany extraneous mixing aids.
Chattopadhyay et al. [10] investigated simultaneous flow develop-ment for circular channel and found no evidence of heat transfer en-hancement in straight ducts. However, the situation was different for
vestigations of developing flow and heat transfer in raccoon type14), http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.04.017
T1:2 Aw wavy amplitude in mmT1:3 A amplitude of pulsating flow, mmT1:4 Dh hydraulic diameter, mmT1:5 f frequency of pulsationT1:6 h average heat transfer coefficientT1:7 k thermal conductivity, W/m-kT1:8 Nuavg average Nusselt numberT1:9 P pressureT1:10 Pr Prandtl numberT1:11 Re Reynolds numberT1:12 St Strouhal numberT1:13 T temperatureT1:14 Uin inlet velocityT1:15 Um mean velocityT1:16 u axial velocity localT1:17
T1:18 Greek symbolsT1:19 Δ difference in the value of variable between inlet andT1:20 outlet of channelT1:21 η enhancement ratioT1:22 λ wave length or pitch of the wavy channel, mT1:23 μ dynamic viscosityT1:24 ρ density of the working fluid, kg/m3
T1:25
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microchannels characterized by low Reynolds number. Nandi andChattopadhyay [11] conducted a study on simultaneously developingflow in a plane and axi-symmetric microchannel in the Reynolds num-ber ranging from 0.1 to 100with a varying amplitude up to 80% and fre-quency up to St = 10. They have observed that the effect of pulsation issignificant only at lowReynolds number compare tomoderate Reynoldsnumber where augmentation due to pulsation is less. Recently, numer-ical study carried out by Nandi and Chattopadhyay [12] on simulta-neously developing flow in a Serpentine type wavy microchannel inthe Reynolds number range of 0.1 ≤ Re ≤ 100. It was observed thatthe pulsation at the inlet was found to enhance heat transfer with areduced pressure drop even at low Reynolds number.
All the above studies of flow in thewavymicrochannel, heat transferenhancement mainly depends on geometry modification, optimizationof amplitude of wavy channel, Reynolds number and transitional com-ponent of the flow. In most of the techniques the desired thermalmixing was often accompanied by a large pressure drop. Otherwise,the improvement in heat transfer was largely marginal. An importantobservationmade is that wavy passage does not provide any significantheat transfer enhancement when the flow is steady, particularly at verylow Reynolds number. However if the flow is made unsteady through
U 4040
Fig. 1. Schematic diagram o
Please cite this article as: T.K. Nandi, H. Chattopadhyay, Numerical inmicrochannels under inlet pulsation, Int. Commun. Heat Mass Transf. (20
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1any external means, significant increase in heat transfer are observed1without relying on roughness of elements, transition to turbulence,1and complicated geometry. Again, it is observed that significant amount1ofwork onmicrochannels has been done both experimentally aswell as1numerically but the literature on simultaneously developing flow in1microchannels is found to be very rare. Further, it is noted that even1for the conventional channels there are conflicting reports in literature1about heat transfer augmentation due to pulsating flow at the inlet.1Accordingly, in this work, study in the grey area of simultaneously1developing flow in microchannels under inlet pulsation is performed.
12. Problem formulation
1Fig. 1 represents a schematic diagram of wavymicrochannel used in1this present investigationwhere D is the hydraulic diameter and L is the1length of the microchannel. There are a number of geometric parame-1ters important to characterize the wavy channel configuration. The tra-1ditional Raccoon channel is modeled where crest and trough are facing1each other by a phase of 00. The height of the modeled channel that1varies sinusoidally is described by the function:
y ¼ Aw sin2πλ
x� �
ð1Þ11
The wave amplitude Aw and wavy length λ are kept constant here1(Aw = 0.2 and λ = 1) to study the impact of pulsating flow at inlet1on thermal performance at this geometry. The nondimensional channel1length was 24 with 1 straight section at the inlet and the outlet. The1wavy section spanned the middle 22 length of the channel with a hy-1draulic diameter of 1. The Prandtl number of the fluid was taken to be17(water). The numerical simulation was performed by solving the1time dependent continuity, momentum and energy equations for a in-1compressible fluid with the following assumptions made; (1)Continu-1ous Newtonian fluid, Reynolds with unsteady laminar flow and heat1transfer, (2) Specific heat, thermal conductivity and viscosity are single1variable functions of temperature, and (3) Negligible gravity and radia-1tion heat transfer. Therefore the governing equations based on these1assumptions are:1Continuity equation:
∂ui
∂t þ∇: ρuð Þ ¼ 0; ð2Þ11
Momentum equation:
∂ui
∂t þ∂ uiuj
� �∂xi
¼ − ∂p∂xi
þ 1Re
∇2uj; ð3Þ11
Energy equation:
∂T∂t þ ui
∂T∂xi
¼ 1Re � Pr
∇2T: ð4Þ11
f a wavy microchannel.
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Fig. 2. Comparison of time average Nusselt number with Re for different amplitudes andsteady cases Q2.
Fig. 3. Comparison of enhancement ratio with varying Strouhal numbers for differentamplitudes Q3(a) Re = 10 (b) Re = 100.
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Isothermal conditions are applied at all microchannelwalls. Both topand bottomwavy surfaces aremaintained at an isothermal temperatureof 330 k. The usual no-slip boundary conditions are applied at the wavywall. At the inlet, the velocity profile is found by adding the uniform ve-locity with a sinusoidal pulsation. Thus the inlet velocity profile is givenby
Uin ¼ um 1þ A sin 2πf tð Þð Þ
where A is the non-dimensional amplitude of pulsation and f (the fre-quency) is defined as f = St um/Dh where St is the non-dimensionalstrouhal number, Dh is thehydraulic diameter andum is themean veloc-ity. At the outlet the continuative boundary condition,where the secondderivative of the primitive variables are set at zero, is employed. Thisensures that there is no abrupt transition at the outlet. This can beexpressed mathematically as:
∂2u∂x2
¼ ∂2v∂x2
¼ ∂2T∂x2
¼ 0: ð5Þ
The heat transfer coefficient for the above type of configuration isgenerally calculated using bulk temperature Tb. In that case, the localheat transfer coefficient h is given by q = h (Tw − Tb). The differentinlet conditions like amplitude and frequency are to be imposed inthis condition.
The value of Nui (x, t) is thus given by:
Nui ¼1
Tw−Tin
∂T∂r jw: ð6Þ
Here suffix i denotes instantaneous value.The time and space averaged values can be obtained by integrating
Nuav ¼ZL
0
ZTP
0
Nui x; tð Þdxdt= LTPð Þ: ð7Þ
The governing equations were solved by using the SIMPLE algo-rithm, a finite volume formulation of Patankar [13]. The expandedform of the governing equation may be found in Chattopadhyay et al.[10].
Grid independences were checked at all Re for developing flow incomparing the results to the solution of the Graetz problem and the an-alytical velocity distribution at the fully developed region. Typically375 × 50 and 375 × 25 grids were used for Re = 0.1, 1, 10 and 100.Grid independencewas ensured by computing at least at three differentgrid levels. The final grid was so chosen that local values differ only byabout 2–4% from the grid independent extrapolated values. According-ly, the grid size of 375 × 50was deemed to be adequate for all the cases.The code is validated by calculating the friction factor at Re = 100 forwavy microchannel of same configuration from Mohammed et al.[14]. The calculated value from the present study is 0.185 while thevalue reported in [14] is 0.2 as shown in Fig. 5.
3. Results and discussion
In the presentwork, investigationswere performedwithin the rangeof 1≤ St≤ 10 and 0.1 b A b 1. The velocity and temperature were mon-itored at several locations during transient calculation to establish thatthe flow field is fully periodic, following the periodic pulsation at theinlet. After that the establishment of periodic time-averaging were car-ried out. For engineering calculations, the most important parametersare the time-averageddata such as time averaged values of Nu and pres-sure drop value in the developing region. In this work, Nusselt numberbased on inlet temperature has been used instead of bulk temperature,following Chattopadhyay et al. [10]. The local bulk temperature is a
Please cite this article as: T.K. Nandi, H. Chattopadhyay, Numerical inmicrochannels under inlet pulsation, Int. Commun. Heat Mass Transf. (20
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variable and hence comparison based on fixed inlet temperature is per-haps a better choice. Fig. 2 shows the comparison of time averaged Nuvalue when the flow is fully developed with different Reynolds numberfor A = 0.2, 0.5 & 0.8 and steady case. It is observed that at very lowReynolds number and low amplitude of pulsation theNu value is almostclose to the steady case (Re ≤ 10 & A = 0.2). This is because at low Reviscous force is predominated than surface geometry effect and no recir-culation could be observed; the flow in the wavy passages is character-ized by a steady flow. However as the Re is increased beyond a modestvalue, the pulsating inlet flow at all amplitude (0≤A≤1) predominatesviscous force which is superimposed with the main flow and the flowbecomes unsteady with the rolling up of the shear layer with the chan-nel wall fluid. The unsteady flow improves themixing process betweenthe core and near-wall fluid resulting in a significant increase in heattransfer compared to steady case.
The pulsation effect is calculated by the enhancement ratio wherethe enhancement ratio is given by η = Nuavg/Nus, Nuavg is time aver-aged value of local Nusselt number at some location and the Nus de-notes the case when the inlet profile is steady for the same location.
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Thus a value of η over 1.0 indicates enhanced heat transfer at the loca-tion. The amplitude of pulsating flow is varied in a range of 0.2 ≤ A≤ 0.8 for three pulsating frequencies 1, 5 &10 are presented in Fig. 3which shows that at low Reynolds number the heat transfer enhance-ment is observed at different pulsating frequencies for amplitudes20%, 50% and 80%, and a sharp increase of enhancement is observedafter frequency 5 for the pulsating amplitude of 80%. There is no recircu-lation existing at very low Reynolds number and the flowwas found tobe essentially streamlined and well contoured along the wall of a wavychannel. At a low frequency and amplitude, boundary layer thinningdue to geometry variation between expansion and contraction sectionis not significant. The heat transfer augmentation happened due tosuperimposing of pulsating flowwith themean flow of channel makingthe flow unsteady enough, causing a good mixing at low Re. At a highvalue of Re, the surface area for the channel geometry considered inthis paper provides only a minor contribution to heat transfer improve-ment but it is the hydrodynamic and thermal boundary layer thinningwhich is more important and the effect is more prominent at a highervalue of amplitude and frequency.
In this work, the important parameter thermal development lengthis investigated at different Reynolds numbers and inlet conditions. Itwas observed that at low Re, the flow stream gets heated up and aftera certain length, temperature gradient ceases to exist. This length is re-ported in Fig. 4, where self sustained oscillation of mean flow and peri-odic inlet pulsation destabilize thermal boundary layer and moreinteraction between near wall fluid and core fluid makes the flow fullydeveloped thermally with shorter entrance region than the steadycase. At a very low Reynolds number, (Re 10) the thermal entry lengthdoes not make any significant difference.
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Fig. 5. Variation of surface averaged friction factors with amplitudes for different Strouhalnumbers at Re = 100.
Please cite this article as: T.K. Nandi, H. Chattopadhyay, Numerical inmicrochannels under inlet pulsation, Int. Commun. Heat Mass Transf. (20
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2strouhal number and amplitude is presented in Fig. 5. The results are2compared to the steady case that is a flow without pulsation.2So it is observed that the present wavymicrochannel with inlet pul-2sating flow can improve the heat transfer performance, albeit with a2marginal increase in pressure drop compared with steady case. At low2Reynolds number the heat transfer enhancement of the present wavy2channels ismarginally ormoderately larger than the pressure drop pen-2alty. At high Reynolds number it can be seen that the heat transfer en-2hancement can potentially be significantly larger than the pressure2drop penalty. The combined effect of heat transfer enhancement and2pressure drop is evaluated through a performance parameter P which2is calculated as the product of enhancement ratio and pressure drop2ratio of steady and pulsatile cases. As such the pumping power is direct-2ly proportional to flow work, therefore reduced pressure drop leads to2saving in energy. It can be seen from Table 1 that at all levels of ampli-2tude and frequency, there is a 5–10% improvement in performance2parameter when pulsation is introduced.
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24. Conclusion
2The objective of thisworkwas to determine the potential heat trans-2fer enhancement for such flow situation over the steady flow. The effect2of changing the strouhal number and amplitude of pulsationwas shown2at different values of Reynolds number. The result shows that heat2transfer enhancement showed maximum at an optimum value of2strouhal number 5 (St=5) and amplitudemore than 50% for lowReyn-2olds number and at high Reynolds, a continuous sharp increase of heat2transfer was observed. Time averaged Nu number was compared with2steady case and shed more light on the changes of Nu when amplitude2and frequency of pulsatingflow changes. The incorporation of a sinusoi-2dal varying velocity component into steady flow in a wavy micro-2channel proves to be good and robust way of enhancing the heat2transfer.
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2References
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[8] Y. Sui, C.J. Teo, P.S. Lee, An experimental study of flow friction and heat transfer inwavy microchannels with rectangular cross section, Int. J. Thermal Sci. 50 (2011)2473–2482.
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